Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers

Ugur Duran; Mehmet Acikgoz

doi:10.20944/preprints201712.0104.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 14 December 2017 / Approved: 15 December 2017 / Online: 15 December 2017 (09:14:10 CET)

In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover (p, q)-extensions of Carlitz's result [L. Carlitz, Mat. Mag., 32 (1959), 247–260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett., 17 (2004), 375–380].

(p, q)-calculus; Bernoulli polynomials; Euler polynomials; Genocchi polynomials; Frobenius-Euler polynomials; generating function; Cauchy product

Computer Science and Mathematics, Algebra and Number Theory

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Apostol Type (p, q)-Frobenius-Euler Polynomials and Numbers

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